Showing papers on "Added mass published in 1991"

Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling

Abstract: An analysis that includes the effects of Basset and gravitational forces is presented for the dispersion of particles experiencing Stokes drag in isotropic turbulence. The fluid velocity correlation function evaluated on the particle trajectory is obtained by using the independence approximation and the assumption of Gaussian velocity distributions for both the fluid and the particle, formulated by Pismen & Nir (1978). The dynamic equation for particle motion with the Basset force is Fourier transformed to the frequency domain where it can be solved exactly. It is found that the Basset force has virtually no influence on the structure of the fluid velocity fluctuations seen by the particles or on particle diffusivities. It does, however, affect the motion of the particle by increasing (reducing) the intensities of particle turbulence for particles with larger (smaller) inertia. The crossing of trajectories associated with the gravitational force tends to enhance the effect of the Basset force on the particle turbulence. An ordering of the terms in the particle equation of motion shows that the solution is valid for high particle/fluid density ratios and to 0(1) in the Stokes number.

Vibration of Circular Plates in Contact With Water

Abstract: The nondimensionalized added virtual mass incremental factors for circular plates having simply-supported, clamped and free edges are obtained by employing the integral transformation technique in conjunction with the dual integral equation method

Numerical predictions of ship motions at high forward speed

Abstract: A theory for ship motions at high forward speed is presented. The theory includes interaction between the steady and unsteady flow field. Numerical results for the steady flow and added mass and damping are compared with experimental results.

Wave forces on three-dimensional floating bodies with small forward speed

Abstract: A boundary-integral method is developed for computing first-order and mean second-order wave forces on floating bodies with small forward speed in three dimensions. The method is based on applying Green's theorem and linearising the Green function and velocity potential in the forward speed. The velocity potential on the wetted body surface is then given as the solution of two sets of integral equations with unknowns only on the body. The equations contain no water-line integral, and the free-surface integral decays rapidly. The Timman-Newman symmetry relations for the added mass and damping coefficients are extended to the case when the double-body flow around the body is included in the free-surface condition. The linear wave exciting forces are found both by pressure integration and by a generalised far-field form of the Haskind relations. The mean drift force is found by far-field analysis. All the derivations are made for an arbitrary wave heading. A boundary-element program utilising the new method has been developed. Numerical results and convergence tests are presented for several body geometries. It is found that the wave exciting forces are presented for several body geometries. It is found that the wave exciting forces and the mean drift forces are most influenced by a small forward speed. Values of the wave drift damping coefficient are computed. It is found that interference phenomena may lead to negative wave drift damping for bodies of complicated shape.

The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion

Abstract: The motion of bubbles dispersed in a liquid when a small‐amplitude oscillatory motion is imposed on the mixture is examined in the limit of small frequency and viscosity. Under these conditions, for bubbles with a stress‐free surface, the motion can be described in terms of added mass and viscous force coefficients. For bubbles contaminated with surface‐active impurities, the introduction of a further coefficient to parametrize the Basset force is necessary. These coefficients are calculated numerically for random configurations of bubbles by solving the appropriate multibubble interaction problem exactly using a method of multipole expansion. Results obtained by averaging over several configurations are presented. Comparison of the results with those for periodic arrays of bubbles shows that these coefficients are, in general, relatively insensitive to the detailed spatial arrangement of the bubbles. On the basis of this observation, it is possible to estimate them via simple formulas derived analytically for dilute periodic arrays. The effect of surface tension and density of bubbles (or rigid particles in the case where the no‐slip boundary condition is applicable) is also examined and found to be rather small.

Coriolis-effect in mass flow metering

Abstract: The paper aims at a detailed description of the physical background, for the so-called Coriolis mass flow meter. It presents essentially an analysis of the (free) vibration modes of a fluid conveying straight pipe segment. Due to the inertial effects of the flowing fluid, mainly the Coriolis force, these modes deviate in shape (and in frequency) from those appearing in the absence of fluid motion. The effect of fluid inertia may, therefore, be exploited for the purpose of flow measurement. The analysis is performed under a simplifying approximation: The pipe is considered as a beam, the fluid as a moving string. This approximation leaves the fluid with only one degree of freedom, connected with its mean velocity, and eliminates an infinity of degrees of freedom of the pipe. Yet it keeps, the essential features of the phenomenon. The equations describing the vibrations are derived variationally, with the constraint of a common vibration amplitude of both fluid and pipe. The Lagrange multiplier associated with the constraint gives the interaction force between pipe and fluid. The modes are determined by a perturbation procedure, wherein the small (perturbation) parameter is related to the fluid velocity. The analysis shows, as main result, how the time delay between the vibrations of two appropriately chosen points of the pipe may serve to determine the mass flow rate of the fluid. Other aspects of the problem, like the precise role of the Coriolis force, are considered. The possible improvement of the used approximation is discussed.

Virtual mass and drag in two-phase flow

Abstract: We study virtual mass and drag effects in a fluid suspension consisting of spherical particles immersed in an incompressible, nearly inviscid fluid. We derive average equations of motion for the fluid phase and the particle phase by the method of ensemble averaging. We show that the virtual mass and drag coefficients may be expressed exactly in terms of the dielectric constant of a corresponding dielectric suspension with the same distribution of particles. We make numerical predictions for the case of an equilibrium distribution of hard spheres.

Prediction of Low Frequency Vibrational Frequencies of Submerged Structures

Abstract: Both finite element and boundary element approaches for calculating fully-coupled added mass matrices are presented and illustrated. The finite element approach is implemented using existing structural analysis capability in NASTRAN. The boundary element approach uses the NASHUA structural acoustics program in combination with NASTRAN to compute the added mass matrix

Interaction between two bodies translating in an inviscid fluid

Abstract: The equations of motion of two bodies in translation motion in an inviscid fluid at rest at infinity are expressed in Lagrangian form. For the case of one body stationary and the other approaching it in a uniform stream, an exact, closed-form solution in terms of added masses is obtained, yielding simple expressions for the velocity of the moving body as a function of its relative position and for the interaction forces. This solution is applied to the case of a rectangular cylinder approaching a cylindrical one, for which the added-mass coefficients had been previously obtained in a companion paper by an integral-equation procedure. In order to compare results with those in the literature, and to evaluate the accuracy of the present procedures, results were calculated for a pair of circular cylinders by these methods as well as by successive images. Very good agreement was found. Comparison with published results showed good agreement with the added mass but very poor agreement on the forces, including disagreement as to whether the forces were repulsive or attractive. The discrepancy is believed to be due to the omission of terms in the Bernoulli equation, which was used to obtain the pressure distribution and then the force on a body. The Lagrangian formulation is believed to be preferable to the pressure-integral approach because it yields the hydrodynamic force directly in terms of the added masses and their derivatives, thus requiring the calculation of many fewer coefficients.

Comparison of numerical calculations of two Biot coefficients with analytical solutions

Abstract: The Biot theory for the acoustics of porous media contains drag and virtual mass coefficients that depend on the physical properties of the fluid and solid constituents, the frequency, and the microstructure of the porous medium. Biot derived an equation for the drag coefficient as a function of frequency by assuming cylindrical pores. In this paper, the finite element method is used to obtain values of the drag and virtual mass coefficients for face‐centered cubic granular materials with three different porosities and compare our numerical results to Biot’s analytical solutions. By making appropriate choices of three parameters in Biot’s analytical solution for cylindrical pores—the pore size parameter, the Kozeny parameter, and the tortuosity—the analytical solution matches these numerical results very well. This suggests that with appropriate choices of these parameters the analytical approach can predict the dependence of the drag and virtual mass coefficients on frequency for an arbitrary pore geometry. These results support a relation suggested by Hovem and Ingram for approximating the pore‐size parameter for spherical grains, and they also agree with a relation suggested by Berryman for the dependence of the tortuosity on the porosity.

Modal Truncation, Ritz Vectors, and Derivatives of Closed-Loop Damping Ratios

Abstract: The effect of modal truncation on the damping ratio and their derivatives with respect to an added mass is investigated for a simply supported, multispan beam with a linear quadratic Gaussian control system. It is found that both the damping ratios and derivatives converge slowly, but the derivatives converge more slowly than the damping ratios. However, it is shown that when Ritz vectors corresponding to static displacements due to actuator forces are added to the reduced model, the convergence of both the damping ratios and their derivatives is accelerated. It is also shown that the accuracy of the damping ratio predicted by a reduced-model control design can be improved significantly if the Ritz vectors are included in the design of the control system. Thus, it appears that Ritz vectors added to the reduced model of flexible structures can improve greatly the accuracy of both the design and analysis of the control system.

Nonlinear Behavior of Articulated Tower in Random Sea

Abstract: An iterative frequency domain method for determining the response of articulated towers to first order wave and current induced forces is presented. The application of the method is illustrated with the help of an idealized articulated tower. The iterative method duly considers the nonlinearities produced due to relative velocity squared drag force, large displacement effect, and variable added mass and buoyancy. The proposed method obtains the nonlinear random response in an efficient manner using fast fourier transform techniques. Using the proposed analysis a parametric study is conducted to investigate the response behavior of the tower to wave and current induced forces.

Acceleration sensitivity of crystal resonators affected by the mass and location of electrodes

Abstract: Predominant thickness-shear frequencies and modes of a crystal plate with electrodes of arbitrary shape and mass distribution are obtained by a finite-element method, based on Mindlin's first-order equations with platings. These frequencies and modes are used in a perturbation method for computing the acceleration sensitivity of crystal resonators with electrodes. Computations are made for a square AT-cut quartz plate that is supported by a four-point mount and coated with identical square and uniform electrodes on the upper and lower faces of the plate. To study the effect of uneven distribution of electrode mass, acceleration sensitivities are calculated when a small mass is added at various locations near the edges of the square electrodes. It is found that the percent increase of the acceleration sensitivity of the resonator with a small added mass to that of the resonator without added mass ranges from 3.8% to 541.7%, depending on the location of the small mass placed at the edges of the electrodes. >

Simplified Earthquake Analysis of Intake-Outlet Towers

Abstract: A simplified procedure is presented to determine the maximum earthquake forces in intake-outlet towers directly from the design earthquake spectrum without the need for a response-history analysis. All the significant effects of tower-water interaction and tower-foundation-soil interaction are included in the analysis. The hydrodynamic effects of outside and inside water are approximated by added mass functions, which can be determined to a useful degree of accuracy without requiring rigorous three-dimensional analysis of the two fluid domains. The simplified response spectrum analysis (SRSA) procedure utilizes convenient methods for computing: (1) The first two natural frequencies and modes of vibration of the tower; and (2) the modifications to the vibration period and the damping ratio of the fundamental vibration mode due to tower-foundation-soil interaction. The procedure is demonstrated to be accurate enough for preliminary design and safety evaluation of towers.

Three-dimensional effects on hydrodynamic forces acting on an oscillating finite-length circular cylinder

Abstract: The hydrodynamic forces acting on finite-length circular cylinders in an oscillating flow was investigated experimentally Forced surging tests were carried out on finite length circular cylinders whose ratio of length to diameter varied from 1 to 10 The drag coefficients, the added mass coefficients and the lift coefficients were obtained, and were compared with those of 2-D circular cylinder and a finite-length circular cylinder with end plates We also studied the flow fields around the circular cylinders using the hydrogen bubble technique

Application of the Discrete Vortex Method to Fluid-Structure Interaction

Abstract: The discrete vortex method for numerical simulation of two-dimensional flows is applied to six problems in fluid-structure interaction: steady flow over bluff and streamlined sections, flow with transverse oscillations of the free stream, oscillation in otherwise still reservoir, vibration induced by steady flow, flow-induced vibration in oscillating flow, and impulsively started flow. Direct comparison is made with various formulations and with experimental data.

Oblique Impact of Two Cylinders in a Uniform Flow

Abstract: The oblique motion of a circular cylinder through an inviscid and incompressible fluid, conveyed by a uniform flow at infinity, in the vicinity of another cylinder fixed in space is considered. In a relative polar co-ordinate system moving with the stream, the kinetic energy of the fluid is expressed as a function of six added masses due to motions parallel and perpendicular to the line joining the centres of the cylinder pair. The Lagrange equations of motion are then integrated for the trajectories of the moving cylinder. In order to evaluate the added masses and their derivatives with respect to the separation distance between the cylinders in terms of the hydrodynamic singularities, the method of successive images, initiated by Hicks, and the Taylor added-mass formula are applied, and analytic solutions in closed form are obtained thereafter. The dynamic behaviour of a drifting body in close proximity of a fixed one is investigated by considering the limiting values of the fluid kinetic energy and the interaction forces on each body. The reliability of the numerical approximation of added masses and their derivatives is also discussed in the present study. The integral equations, in terms of surface source distributions and also discussed in the present study. The integral equations, in terms of surface source distributions and their derivatives on both circles, are carefully modified for obtaining accurate numerical solutions.

Forced oscillation experiments

Abstract: Forced oscillation experiments with scale models are carried out to determine hydrodynamic characteristics of ships, with respect to motions in waves or steering and manoeuvring qualities. Depending on the considered motion components, in a horizontal or vertical plane, v-arious methods are used to induce forced oscillations which are discussed briefly. Some results of forced oscillation experiments are presented as examples of this technique and compared with calculations based on numerical methods. The comparisons include, among others, the effects of ship speed and restricted water depth. Forced oscillation experiments with scale models are used in ship research for the determination of hydrodynamic forces associated with oscillatory motions of ships and other maritime constructions. The results obtained with oscillating models have been used to determine the coefficients of the equations of motion, for instance to validate theoretical models of the considered dynamic flow problems. These have included simplified engineering solutions for the prediction of the motion of a ship advancing in irregular sea waves, as well as advanced numerical three-dimensional methods for the determination of hydrodynamic forces, based on rational theories. In these oscillation techniques a scale model is forced to carry out harmonic oscillations of known amplitude and frequency. The required force is split up in a component in phase with the motion of the body to obtain the hydrodynamic or added mass, whereas the quadrature component is associated with damping. The experiment may concern one particular mode of motion, for instance heaving of a ship, or more complicated coupled motions, generated by a so-called planar motion mechanism, to obtain linear and nonlinear hydrodynamic coefficients of the equations of motion in a horizontal plane for the simulation of steering and manoeuvring of ships. As far as I know the first published forced oscillation experiment with a ship model has been carried out by iHaskind & Rieman (1946). Forced heaving motions at zero forward speed were carried out in a range of frequencies and amplitudes of motion. The results showed frequency-dependent damping, vanishing at high and low frequencies, and frequency dependent hydrodynamic mass. The influence of nonlinearities appeared to be small for the considered wall-sided mathematical ship model. Later similar techniques have been used in various ship hydrodynamic laboratories as a consequence of the increased interest in the dynamics of ships. Some results of forced oscillation experiments, carried out in the Delft Shiphydrodynamic Laboratory, are briefly summarized here to illustrate the

軸対称物体のすきま流れ振動 : 第1報, 軸対称物体に及ぼす流体力の解析

Abstract: An analytical investigation is presented on leakage-flow-induced vibrations of an axisymmetric body. In the case of a narrow annular passage between a tapered outer cylinder and a tapered axisymmetric body, the fluid-dynamic forces exerted on the body were calculated by Galerkin's method. From the calculated results, the following conclusions were obtained. The dynamic instability of the systems is due to phaselag of the fluid-dynamic force for the harmonic vibration of the body. The fluid-dynamic damping is obtained in two parts: one is independent of the frequency and the other is a function of the frequency, and the negative damping is caused by the fluid-dynamic damping which is a function of the frequency. When the frequency is very large, the fluid-dynamic mass agrees with the added mass within the rest fluid.

The Shape-Effect Of Buffer On The Longitudinal Vibration Of A Pipe-String In The Deep Sea

Abstract: In order to analyze the longitudinal vibration of the pipe-string in the deep sea, first, the drag and added mass coefficients of various buffer-models vibrating axially in water were evaluated by the method developed by the authors. Then, the forced longitudinal vibration of the pipe-string equipped with a pump-module and a buffer was analyzed theoretically by introducing the fluid forces evaluated with the above-obtained coefficients. Furthermore, the axial stress induced in the pipe-string was calculated. The results indicate that the buffer whose shape causes a higher drag force is more useful for reducing the amplitude of the vibration and the axial stress in the pipe-string, and that the highest-drag buffer used in this study causes a half amplitude of the vibration and about 63% axial stress at the first resonance as compared with those produced by the lowest-drag model.

Modelling and control of a marine robot arm

Abstract: The model of a robot arm intended for underwater tasks is defined. The model presented was obtained by introducing the hydrodynamic effects, which were calculated according to the equation of Morison (in J.F. Wilson, Ed., 1989) in the derivation of the equations of motion. The most important hydrodynamic influence on the arm dynamics is related to the added mass concept, which originates a virtual mass mechanism. This has as a consequence a large increment on the control input. The simulation presented shows that the nonlinear variable structure system is robust with hydrodynamic interaction. >

Stochastic responses of anchored flexible floating islands subjected to wind-waves and seaquakes

Abstract: This paper is concerned with a unified approach which predicts the stochastic responses of a flexible floating island, anchor system and sea water. The floating island is modelled as an elastic circular plate and the anchor system is considered to be composed of distributed tension-legs. Based on a linear potential flow theory, the hydrodynamic pressure generated on the bottom surface of the island is obtained in closed form. The modal equations of motion of the island with or without anchor system is derived by energy method. In the formulation, the dynamic interaction effects are estimated as hydrodynamic added mass, hydrodynamic added damping and hydrodynamic added stiffness. The response quantities are evaluated as root-mean-squared values using a linear random vibration theory. Numerical examples are presented to discuss the effects of hydrodynamic radiation damping, anchor system, and wind-wave and seaquake characteristics on the stochastic responses of flexible floating islands.

Response of articulated towers to viscous drift forces

Abstract: The response behaviour of an articulated tower to low frequency drift forces in random sea is investigated. The drift force is considered to be proportional to the square of the wave elevation and is simulated using a drift force coefficient and the time history of slowly varying wave envelope in random sea. The drift force coefficient is determined for the tower being analysed using its response to regular waves of different periods combined with current velocity and mass transport velocity. The responses to second-order drift forces are obtained in the time domain by incorporating the nonlinearities produced by the variable added mass and the variable buoyancy effects. An example problem is solved under different random sea states and the results are analysed for characterising the random behaviour of both the exciting force and the response. Also, the importance of the response of the articulated towers excited by the viscous drift forces is shown by comparing it with the response produced by first-order wave force.

Wave loading on ships and platforms at a small forward speed

Abstract: Forces on marine structures oscillating incoming waves with a small forward speed are studied. Coupling between the oscillatory wave field and the steady flow around the body is accounted for. Friction and separation effects are disregarded, and the fluid flow is modelled by potential theory. The boundary value problem for the velocity potential is transformed to an integral equation by Green's theorem, using a Green function satisfying the linear free surface condition with small forward speed. This integral equation contains unknowns on the wetted body surface and on a region of the free surface close to the body. Local, small forward speed expansions for the potential and the Green function are introduced in the vicinity of the body, giving two sets of integral equations for the unknown zero speed and the small forward speed potentials. These integral equations contain unknowns on the wetted body surface only. The right hand side of the small forward speed integral equation involves a fast decaying integral over the free surface. There is no water line integral in the integral equations. The method is applicable to bodies of arbitrary shape. The diagonal added mass and damping coefficients are found to be functions of the forward speed only through the encounter frequency. This linear exciting forces are found by generalised Haskind relations. The mean second order horizontal drift forces and the mean second order yaw moment are discussed, and numerical examples are presented for a ship and a platform. The mean drift forces are usually increased by a small forward speed against the incoming wave direction. For complex body geometries the wave drift damping may, however, in narrow wave number regions, become negative. Numerical examples show that the mean drift force and the mean yaw moment may be changed by 100% even for a small forward speed.

Forces on a wave-energy module

Abstract: Mathematical models for the calculation of wave forces added mass and radiation damping of a wave energy module is developed in order to assess the energy take-out. The module consists of a buoy connected to a submerged plate by a so-called hose pump. In the present models the buoy and the submerged plate are idealized to two cylinders of equal radii. The presented method is founded on the method of matched eigenfunction expansion. Comparisons with other solutions are presented and the agreement is shown to be satisfactory. The developed models are computer efficient and will be used in an optimization procedure for a wave climate.